Part of the Atlas of Small Regular Polytopes

Polytope of Type {24,3}

Atlas Canonical Name {24,3}*576

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(576,5053)
Rank
3
Schläfli Type
{24,3}
Vertices, edges, …
96, 144, 12
Order of s0s1s2
6
Order of s0s1s2s1
24
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

3-fold

4-fold

12-fold

16-fold

24-fold

48-fold

Covers minimal covers in bold

2-fold

3-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s2*(s1*s0)^5*s2*(s1*s0)^2*s1*s2> of order 2

8 facets

48 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2> of order 2

6 facets

48 vertex figures

P/N, where N=<s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4

4 facets

24 vertex figures

P/N, where N=<(s0*s1)^6> of order 4

6 facets

24 vertex figures

P/N, where N=<(s0*s1)^2*s0*s2*(s1*s0)^2*s2, s0*s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 4

4 facets

24 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,41)(18,42)(19,43)(20,44)(21,48)(22,47)(23,46)(24,45)(25,33)(26,34)(27,35)(28,36)(29,40)(30,39)(31,38)(32,37);;
s1 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)(10,24)(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(35,36)(37,44)(38,43)(39,41)(40,42)(45,46);;
s2 := ( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)(20,34)(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)(31,38)(32,39);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,16)( 6,15)( 7,14)( 8,13)(17,41)(18,42)(19,43)(20,44)(21,48)(22,47)(23,46)(24,45)(25,33)(26,34)(27,35)(28,36)(29,40)(30,39)(31,38)(32,37);
s1 := Sym(48)!( 1,17)( 2,18)( 3,20)( 4,19)( 5,28)( 6,27)( 7,25)( 8,26)( 9,23)(10,24)(11,22)(12,21)(13,30)(14,29)(15,31)(16,32)(35,36)(37,44)(38,43)(39,41)(40,42)(45,46);
s2 := Sym(48)!( 2, 4)( 5,14)( 6,15)( 7,16)( 8,13)(10,12)(17,33)(18,36)(19,35)(20,34)(21,46)(22,47)(23,48)(24,45)(25,41)(26,44)(27,43)(28,42)(29,40)(30,37)(31,38)(32,39);
poly := sub<Sym(48)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle